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  <div class="section" id="numpy-nper">
<h1>numpy.nper<a class="headerlink" href="#numpy-nper" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.nper">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">nper</code><span class="sig-paren">(</span><em class="sig-param">rate</em>, <em class="sig-param">pmt</em>, <em class="sig-param">pv</em>, <em class="sig-param">fv=0</em>, <em class="sig-param">when='end'</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/financial.py#L271-L349"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.nper" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the number of periodic payments.</p>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 1.18: </span><a class="reference internal" href="#numpy.nper" title="numpy.nper"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nper</span></code></a> is deprecated; for details, see NEP 32 <a class="reference internal" href="#rc337c54a0685-1" id="id1">[1]</a>.
Use the corresponding function in the numpy-financial library,
<a class="reference external" href="https://pypi.org/project/numpy-financial">https://pypi.org/project/numpy-financial</a>.</p>
</div>
<p><a class="reference external" href="https://docs.python.org/dev/library/decimal.html#decimal.Decimal" title="(in Python v3.9)"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> type is not supported.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>rate</strong><span class="classifier">array_like</span></dt><dd><p>Rate of interest (per period)</p>
</dd>
<dt><strong>pmt</strong><span class="classifier">array_like</span></dt><dd><p>Payment</p>
</dd>
<dt><strong>pv</strong><span class="classifier">array_like</span></dt><dd><p>Present value</p>
</dd>
<dt><strong>fv</strong><span class="classifier">array_like, optional</span></dt><dd><p>Future value</p>
</dd>
<dt><strong>when</strong><span class="classifier">{{‘begin’, 1}, {‘end’, 0}}, {string, int}, optional</span></dt><dd><p>When payments are due (‘begin’ (1) or ‘end’ (0))</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The number of periods <code class="docutils literal notranslate"><span class="pre">nper</span></code> is computed by solving the equation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fv</span> <span class="o">+</span> <span class="n">pv</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">rate</span><span class="p">)</span><span class="o">**</span><span class="n">nper</span> <span class="o">+</span> <span class="n">pmt</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">rate</span><span class="o">*</span><span class="n">when</span><span class="p">)</span><span class="o">/</span><span class="n">rate</span><span class="o">*</span><span class="p">((</span><span class="mi">1</span><span class="o">+</span><span class="n">rate</span><span class="p">)</span><span class="o">**</span><span class="n">nper</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">=</span> <span class="mi">0</span>
</pre></div>
</div>
<p>but if <code class="docutils literal notranslate"><span class="pre">rate</span> <span class="pre">=</span> <span class="pre">0</span></code> then:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fv</span> <span class="o">+</span> <span class="n">pv</span> <span class="o">+</span> <span class="n">pmt</span><span class="o">*</span><span class="n">nper</span> <span class="o">=</span> <span class="mi">0</span>
</pre></div>
</div>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="rc337c54a0685-1"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
<dd><p>NumPy Enhancement Proposal (NEP) 32,
<a class="reference external" href="https://numpy.org/neps/nep-0032-remove-financial-functions.html">https://numpy.org/neps/nep-0032-remove-financial-functions.html</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>If you only had $150/month to pay towards the loan, how long would it take
to pay-off a loan of $8,000 at 7% annual interest?</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">nper</span><span class="p">(</span><span class="mf">0.07</span><span class="o">/</span><span class="mi">12</span><span class="p">,</span> <span class="o">-</span><span class="mi">150</span><span class="p">,</span> <span class="mi">8000</span><span class="p">),</span> <span class="mi">5</span><span class="p">))</span>
<span class="go">64.07335</span>
</pre></div>
</div>
<p>So, over 64 months would be required to pay off the loan.</p>
<p>The same analysis could be done with several different interest rates
and/or payments and/or total amounts to produce an entire table.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">nper</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ogrid</span><span class="p">[</span><span class="mf">0.07</span><span class="o">/</span><span class="mi">12</span><span class="p">:</span> <span class="mf">0.08</span><span class="o">/</span><span class="mi">12</span><span class="p">:</span> <span class="mf">0.01</span><span class="o">/</span><span class="mi">12</span><span class="p">,</span>
<span class="gp">... </span>                   <span class="o">-</span><span class="mi">150</span>   <span class="p">:</span> <span class="o">-</span><span class="mi">99</span>     <span class="p">:</span> <span class="mi">50</span>    <span class="p">,</span>
<span class="gp">... </span>                   <span class="mi">8000</span>   <span class="p">:</span> <span class="mi">9001</span>    <span class="p">:</span> <span class="mi">1000</span><span class="p">]))</span>
<span class="go">array([[[ 64.07334877,  74.06368256],</span>
<span class="go">        [108.07548412, 127.99022654]],</span>
<span class="go">       [[ 66.12443902,  76.87897353],</span>
<span class="go">        [114.70165583, 137.90124779]]])</span>
</pre></div>
</div>
</dd></dl>

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